EXAM 1                     March 13, 1991            PS 208                    
                                                                               
                                                                               
    If you need a constant not given here or do not understand                 
                                                                               
a problem, please ask me about it.  No notes, books, etc. may                  
                                                                               
be used during this exam.                                                      
                                                                              
                 2                                -19                         
    g = 9.8 m/sec                     e = 1.6 x 10    C                        
                                                                               
                                 9    2    2                                   
     1/(4 pi epsilon ) = 9.1 x 10  N m  / C                                    
                    0                                                          
                                                                               
                      -7                                                       
     mu  / (4 pi) = 10   T m/ A                                                
       0                                                                       
                                                                               
                                           -31                                 
     The mass of the electron is 9.11 x 10     kg.                             
                                                                               
         1. [10 points]                                                        
                                                                               
           (a).  Describe a good way to reconstruct Coulomb's Law              
                                                                               
without memorization.  You need not have a technique for finding               
                                                                               
the arbitrary form of the constant, and you may use anything                   
                                                                               
in the heading of this exam.                                                   
                                                                               
                                                                               
            (b).  Explain a good technique for determining                     
                                                                               
without memorization how to determine the constant in Gauss's                  
                                                                               
Law.  You may assume that you know Coulomb's Law.                              
                                                                               
                                                                               
        2.  A charge of  -3Q  is at the origin of coordinates.                 
                                                                               
Where must a charge  +Q  be placed on the x axis if the combined               
                                                                               
field is to be zero at a point  x = +b  on the axis?                           
                                                                               
        3.  A proton (mass  m ) is shot out along the x                        
                             p                                                 
                                                                               
axis from the origin with a speed  v .  In                                     
                                    0                                          
                                                                               
this region, there is a constant electric field of magnitude                   
                                                                               
                     ^                                                         
 E  pointed in the  -x  direction.  How far                                    
                                                                               
                                                                               
from the origin does the proton get before it stops?                           
                                                                               
                                                                               
   4 (From homework).  A solid nonconducting sphere of radius                  
                                                                               
r   has a total charge  Q  which is distributed according                      
 0                                                                             
to  rho  = br , where  rho  is the charge per                                  
                                                                               
unit volume (charge density) and  b  is a constant.  Determine                 
                                                                               
the electric field at all points inside the sphere.  Notice                    
                                                                               
that  rho   cannot be taken out of radial integrations,                        
                                                                               
but is a constant with respect to angular integrations.  [If                   
                                                                               
you have trouble with  dV, write out the closest form you can                  
                                                                               
and box it so I will know what you are using.]